Spatially and/or temporally extended nonlinear systems characterized by collective properties associated with the system as a whole--and that are different from the characteristic behaviors of the constituent parts.(From the FAQ sheet of the sci.nonlinear newsgroup)

A complex system is a system whose properties are not fully explained by an understanding of its component parts. Complex systems consist of a large number of mutually interacting and interwoven parts, entities or agents. They are woven out of many parts, the Latin complexus comes from the Greek pleko or plektos, meaning "to plait or twine." (Gell-Mann). Complex systems is also often used as a broad term addressing a research approach which includes ideas and techniques from chaos theory, artificial life, evolutionary computation and genetic algorithms.....

A complex system is composed of several elements interacting among them. The complexity of a system depends on the number of elements that conform it, the number of interactions among the elements, and the complexities of the elements and the interactions. (See Section 2.1.)

a network of component nodes that share knowledge with each other and adapt their behavior in order to collaborate to achieve global system goals that could not be achieved alone by any individual node

One not describable by a single rule. Structure exists on many scales whose characteristics are not reducible to only one level of description. Systems that exhibit unexpected features not contained within their specification. Systems with multiple objectives.

There are many definitions of complexity, therefore many natural, artificial and abstract objects or networks can be considered to be complex systems, and their study (complexity science) is highly interdisciplinary. Examples of complex systems include ant-hills, ants themselves, human economies, nervous systems, cells and living things, including human beings, as well as modern energy or telecommunication infrastructures.